A "flat/steep band" model for superconductivity

Based on a viewpoint of chemical pairwise interactions between electrons, a Hamiltonian was proposed for the "flat/steep band" scenario. This model has been studied analytically, and numerically with the first-principles method. With Hg and MgB2 as examples, we have explained the characteristics of this model and observed peak-like structures of the electron-phonon coupling constants lambda(q) in q space. The strong coupling of the "flat band" electrons with phonons has been corroborated by developing a new functional Psib(Phi), through which we can quantitatively compare different electronic states in coupling to a specific phonon. The relevance of our model to an electronic inhomogeneity is also discussed. Investigations on experimental and theoretical low-energy electronic structures of superconductors support our flat/steep scenario.